Water waves diffraction by a submerged sphere and dual integral transforms

A solution of the diffraction problem for a submerged sphere in finite water depth based on the linearized potential theory is presented. The sphere can take different positions relative to the bottom. A new method is suggested to solve this problem. This method is a generalization of the integral transforms. Two systems of the curvilinear coordinates are used, two spectral systems are constructed and two spectral functions are introduced to obtain the solution. For the first spectral function an integral representation is obtained, for the second spectral function an integro-operator equation is derived. Different asymptotic approximations are considered.